Are yields for organic farming different from conventional farming yields? Independent random samples from method A (organic farming) and method B (co

geduiwelh 2020-11-08 Answered
Are yields for organic farming different from conventional farming yields? Independent random samples from method A (organic farming) and method B (conventional farming) gave the following information about yield of sweet corn (in tons/acre). MethodA:6.51,7.02,6.81,7.27,6.73,6.11,6.17,5.88,6.69,7.12,5.74,6.90.
MethodB:7.32,7.01,6.66,6.85,5.78,6.48,5.95,6.31,6.50,5.93,6.68. Use a 5% level of significance to test the claim that there is no difference between the yield distributions. (a) What is the level of significance? (b) Compute the sample test statistic. (Round your answer to two decimal places.) (c) Find the P-value of the sample test statistic. (Round your answer to four decimal places.)
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falhiblesw
Answered 2020-11-09 Author has 97 answers

From the given data: x1=x1n1=78.9512=6.579
s1=0.4992
x2=x1=x2n2=71.4711=6.497
s2=0.4791 Calculating pooled standard deviation: sp=s12(n11)+s22(n21)n1+n22=0.49922×11+0.47912×1012+112=0.4897
H0:μ1=μ2
HA:μ1μ2

a) Leve of significance=0.05

b) Test Statistics: t=x1x2sp×1n1+1n2=6.5796.4970.4897×112+111=0.40

c)P-value for a two tailed test: Degree of freedom =n1+n22=12+112=21 Using t-distribution table P-value =0.6932 As P-value is more than the significance level, we do not have sufficient evidence to reject H0 Conclusion: There is no difference between the yield distributions.

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